Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System

Candy T, Herr S (2018)
Analysis & PDE 11(5): 1171-1240.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Firstly, bilinear Fourier restriction estimates - which are well known for free waves - are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications to nonlinear dispersive equations, in particular in the presence of resonances. Secondly, critical global well-posedness and scattering results for massive Dirac-Klein- Gordon systems in dimension three are obtained, in resonant as well as in nonresonant regimes. The results apply to small initial data in scale-invariant Sobolev spaces exhibiting a small amount of angular regularity.
Stichworte
bilinear Fourier restriction; adapted function spaces; quadratic; variation; atomic space; Dirac-Klein-Gordon system; resonance; global; well-posedness; scattering
Erscheinungsjahr
2018
Zeitschriftentitel
Analysis & PDE
Band
11
Ausgabe
5
Seite(n)
1171-1240
eISSN
1948-206X
Page URI
https://pub.uni-bielefeld.de/record/2920707

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Candy T, Herr S. Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System. Analysis & PDE. 2018;11(5):1171-1240.
Candy, T., & Herr, S. (2018). Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System. Analysis & PDE, 11(5), 1171-1240. doi:10.2140/apde.2018.11.1171
Candy, T., and Herr, S. (2018). Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System. Analysis & PDE 11, 1171-1240.
Candy, T., & Herr, S., 2018. Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System. Analysis & PDE, 11(5), p 1171-1240.
T. Candy and S. Herr, “Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System”, Analysis & PDE, vol. 11, 2018, pp. 1171-1240.
Candy, T., Herr, S.: Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System. Analysis & PDE. 11, 1171-1240 (2018).
Candy, Timothy, and Herr, Sebastian. “Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System”. Analysis & PDE 11.5 (2018): 1171-1240.

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arXiv: 1605.04882

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